Seven digits from the digits $1,2,3,4,5,6,7,8,9$ are written in a random order. The probability that this seven digit number is divisible by 9 is.

$1,2,3,4,5,6,7,8,9$

$\Rightarrow \left(1,8\right),\left(2,7\right),\left(3,6\right),\left(4,5\right),9$

Favorable ways= Taking 3 in first four system 4 last one

$=4C_3\times 1=4$

Total ways $=9C_7=36$

$\therefore$ Required probability$=\frac{4}{36}=\frac{1}{9}$